Effective manipulation across diverse objects is critical for applications ranging from agricultural harvesting to laboratory and domestic automation. While the inherent compliance of soft robotics is well suited to this challenge, designing grippers that generalize across tasks remains difficult due to the vast design space of continuum mechanics and the risk of overfitting to specific scenarios. We propose a graph-based design space for representing soft structures and mechanisms, coupled with a multi-objective, diversity-driven genetic optimization framework that explicitly promotes solution variety throughout the design process. Using multiple grasping scenarios during optimization, we study how task diversity influences the emergence of generalization to unseen objects and contact conditions. Our results show that optimization over a sufficiently diverse set of grasping cases leads to designs with emergent generalization, exhibiting improved robustness compared to task-specific solutions on novel scenarios. These findings suggest that diversity-driven optimization offers a principled pathway toward general-purpose soft grippers, aligned with the adaptable nature of soft robotics.

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